How do you find the common ratio for #64,-32,16,-8,4,...#?

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Answer 1 · 2016-09-21T12:08:44

Common ratio is #-1/2#

In a Geometric series, common ratio is the ratio of a term with respect to its preceding term.

Here we have the series #{64,-32,16,-8,4,.................}#

and hence common ratio is #-32/64=16/(-32)=-8/16=4/(-8)=-1/2#

Answer 2 · 2016-09-21T12:14:03

Common ratio: #color(green)(-1/2)#

Let the ratio between successive terms #a_n# and #a_(n+1)# be #r_n=(a_(n+1))/(a_n)#

Then for the given terms: #64,-32,16,-8,4, ...#
#color(white)("XX")r_1=(-32)/64 = -1/2#

#color(white)("XX")r_2=16/(-32) = -1/2#

#color(white)("XX")r_3=(-8)/16= -1/2#

#color(white)("XX")r_4=4/(-8) = -1/2#

assuming this pattern holds for subsequent (unspecified) terms,
we can see that there is a common ration of #(-1/2)#